Clamped Cubic Spline Interpolating Polyonomial. More...
Static Public Member Functions | |
| static | interpolate ($source,... $args) |
| Interpolate. More... | |
| static | getSplinePoints ($source, array $args=[]) |
| Determine where the input $source argument is a callback function, a set of arrays, or neither. More... | |
| static | validateSpline (array $points, $degree=2) |
| Validate that there are enough input arrays (points), that each point array has precisely three numbers, and that no two points share the same first number (x-component) More... | |
 Static Public Member Functions inherited from MathPHP\NumericalAnalysis\Interpolation\Interpolation | |
| static | getPoints ($source, array $args=[]) |
| Determine where the input $source argument is a callback function, a set of arrays, or neither. More... | |
| static | validate (array $points, $degree=2) |
| Validate that there are enough input arrays (points), that each point array has precisely two numbers, and that no two points share the same first number (x-component) More... | |
Public Attributes | |
| const | Y’ = 2 |
| Public Attributes inherited from MathPHP\NumericalAnalysis\Interpolation\Interpolation | |
| const | X = 0 |
| const | Y = 1 |
Static Protected Member Functions | |
| static | functionToSplinePoints (callable $function, callable $derivative, $start, $end, $n) |
| Evaluate our callback function and derivative at n evenly spaced points on the interval between start and end. More... | |
| Static Protected Member Functions inherited from MathPHP\NumericalAnalysis\Interpolation\Interpolation | |
| static | functionToPoints (callable $function, $start, $end, $n) |
| Evaluate our callback function at n evenly spaced points on the interval between start and end. More... | |
| static | sort (array $points) |
| Sorts our coordinates (arrays) by their x-component (first number) such that consecutive coordinates have an increasing x-component. More... | |
Detailed Description
Clamped Cubic Spline Interpolating Polyonomial.
In numerical analysis, cubic splines are used for polynomial interpolation.
A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points." In the case of the Clamped cubic spline, the first derivative of piecewise polynomial is set to equal the first derivative of our input at the endpoints.
Cubic spline interpolation belongs to a collection of techniques that interpolate a function or a set of values, producing a continuous polynomial. In the case of the cubic spline, a piecewise function (polynomial) is produced. We can either directly supply a set of inputs and their corresponding outputs for said function, or if we explicitly know the function, we can define it as a callback function and then generate a set of points by evaluating that function at n points between a start and end point. We then use these values to interpolate our piecewise polynomial.
https://en.wikipedia.org/wiki/Spline_interpolation http://mathworld.wolfram.com/CubicSpline.html
Member Function Documentation
◆ functionToSplinePoints()
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staticprotected |
Evaluate our callback function and derivative at n evenly spaced points on the interval between start and end.
- Parameters
-
callable $function f(x) callback function callable $derivative f'(x) callback function number $start the start of the interval number $end the end of the interval number $n the number of function evaluations
- Returns
- array
◆ getSplinePoints()
|
static |
Determine where the input $source argument is a callback function, a set of arrays, or neither.
If $source is a callback function, run it through the functionToPoints() method with the input $args, and set $points to output array. If $source is a set of arrays, simply set $points to $source. If $source is neither, throw an Exception.
- Todo:
Add method to verify function is continuous on our interval
Add method to verify input arguments are valid. Verify $start and $end are numbers, $end > $start, and $points is an integer > 1
- Parameters
-
callable | array $source The source of our approximation. Should be either a callback function or a set of arrays. array $args The arguments of our callback function: derivative, start, end, and n. Example: [$derivative, 0, 8, 5]. If $source is a set of arrays, $args will default to [].
- Returns
- array
- Exceptions
-
Exception
◆ interpolate()
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static |
Interpolate.
- Parameters
-
callable | array $source The source of our approximation. Should be either a callback function or a set of arrays. Each array (point) contains precisely three numbers: x, y, and y' Example array: [[1,2,1], [2,3,0], [3,4,2]]. Example callback: function($x) {return $x**2;} number ... $args (Optional) An additonal callback: our first derivative, and arguments of our callback functions: start, end, and n. Example: approximate($source, $derivative, 0, 8, 5). If $source is a set of points, do not input any $args. Example: approximate($source).
- Returns
- Piecewise The interpolting (piecewise) polynomial, as an instance of Piecewise.
◆ validateSpline()
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static |
Validate that there are enough input arrays (points), that each point array has precisely three numbers, and that no two points share the same first number (x-component)
- Parameters
-
array $points Array of arrays (points) number $degree The miminum number of input arrays
- Returns
- bool
- Exceptions
-
Exception if there are less than two points Exception if any point does not contain three numbers Exception if two points share the same first number (x-component)
The documentation for this class was generated from the following file:
- src/NumericalAnalysis/Interpolation/ClampedCubicSpline.php
